A high-speed algorithm for computation of fractional differentiation and fractional integration

Abstract

A high-speed algorithm for computing fractional differentiations and fractional integrations in fractional differential equations is proposed. In this algorithm, the stored data are not the function to be differentiated or integrated but the weighted integrals of the function. The intervals of integration for the memory can be increased without loss of accuracy as the computing time-step n increases. The computing cost varies as n log n, as opposed to n2 of standard algorithms. © 2013 The Author(s) Published by the Royal Society. All rights reserved.